This study presents a novel approach that combines agricultural census data with remotely sensed time series to develop accurate predictive models for paddy rice yield across the different regions of Peru. By leveraging sparse regression and Elastic-Net regularization techniques, the study uncovers causal relationships between key remotely sensed variables such as Normalized Difference Vegetation Index (NDVI), precipitation (PREC), temperature (TEMP), and agricultural yield. To further enhance prediction accuracy, first- and second-order dynamic transformations (velocity and acceleration) of these variables were applied to capture non-linear patterns and lagged effects on yield. The findings demonstrate improved predictive performance when integrating regularization techniques with climatic and geospatial variables, allowing for more accurate forecasts of yield variability. The results confirm the presence of causal relationships in the Granger sense, underscoring the value of this methodology to strategic agricultural management. This contributes to more efficient and sustainable production in paddy rice cultivation.

Interpreting the noise in a stochastic differential equation, in particular the Itô versus Strato-novich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of noise, given by the so-called Hänggi–Klimontovich integral, has been proposed as better adapted to describe certain physical systems, particularly in statistical mechanics. Herein, we introduce this integral in a precise mathematical manner and analyze its properties, signaling those that have made it appealing within the realm of physics. Subsequently, we employ this integral to model some statistical mechanical systems, such as the random dispersal of Langevin particles and the relativistic Brownian motion. We show that, for these classical examples, the Hänggi–Klimontovich integral is worse adapted than the Itô integral and even the Stratonovich one.

We introduce “stochastic cloaking,” where a region of space is concealed from an ensemble of diffusing particles whose individual trajectories are governed by a stochastic (Langevin) equation. Our simulations reveal how different interpretations of the Langevin equation affect the cloaking performance of an annular single-layer invisibility cloak of smoothly varying diffusivity in two dimensions. Near-perfect cloaking is achieved under the Itô convention, indicated by the cloak preventing particles from accessing an inner core without disturbing the particle density outside the cloak. The cloak's performance can be further improved by regularizing its singular behavior. We believe our demonstration of stochastic cloaking is a significant milestone, comparable to earlier developments that extended cloaking from optics and acoustics to thermodynamics.

Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the probability density of the stochastic process that solves a corresponding stochastic differential equation. The kinetic interpretation of noise refers to a prospective notion of stochastic integration that would connect a stochastic differential equation with a Fokker-Planck equation consistent with the Fick law of diffusion, without introducing correction terms in the drift. This work is devoted to identifying the precise conditions under which such a correspondence can occur. One of these conditions is a structural constraint on the diffusion tensor, which severely restricts its possible form and thereby renders the kinetic interpretation of noise a non-generic situation. This point is illustrated through a series of examples. Furthermore, the analysis raises additional questions, including the possibility of defining a stochastic integral inspired by numerical algorithms, the behavior of stochastic transport equations in heterogeneous media, and the development of alternative models for anomalous diffusion. All these topics are addressed using stochastic analytical tools similar to those employed to study the main problem: the existence of the kinetic interpretation of noise.